Thermal Management Aboard the ITS

Between Elon Musk’s announcement of his architecture to send humans to Mars, and the community questions he answered last week, we now have a much better idea how such a trip will work. This enables intelligent discussion of many possible facets of such a mission, but the one we want to discuss today is heat management. Unlike on Earth, spacecraft are relatively thermally isolated things, losing heat only by radiation into space, and gaining heat only from sunlight.

There is also the issue of cryogenic propellant storage. Not only do the humans at the front  of the craft have to kept at a comfortable temperature,  the tanks of liquid oxygen and liquid methane have to be kept no warmer that their contents’ respective boiling temperatures of 90 Kelvin (-180°C, -300°F) and 110 Kelvin (-160°C, -260°F). Some of the liquid is expected to boil off during flight, but most of it is needed for the propulsive part of Mars descent (on the way back, this is a little less of a worry – if all the fuel boiled off, you could, in principle at least, use aerocapture on Earth return, and then refuel the spacecraft in Earth orbit).

There was a good discussion earlier today (on the r/SpaceX subreddit) on some of the issues surrounding thermal management. The thread uses values from NASA’s conceptual TransHab module (plus some estimation) to find the heat produced by the spaceship’s systems. However, there is an alternative, and perhaps simpler way to perform the same calculation. We know [1] that at Earth departure, the solar panels produce 200kW of power. If the efficiency of solar panels was constant with light intensity, we can calculate [2] that they would produce about 90 kW in Mars orbit. In reality, solar panels get less efficient at lower intensities, so the actual power produced will be a little lower than that. So (unless there is also a nuclear reactor that SpaceX haven’t told us about yet), all of the systems on board (regardless of number of crew) will have to use no more than 90kW of electricity between them, and correspondingly, give off no more than 90kW of heat.

What about the heat from the solar panels? A good solar panel from one of Musk’s other companies, SolarCity, would be on the order 22% efficient [3] at converting light into electricity, converting most of the remaining energy to heat. Admittedly, this is a very mass-produced panel, and the ones on the ITS will more than likely be more efficient than that. In fact, if you calculate their efficiency from the 200kW given by SpaceX [1] and their estimated area, you get 26.1% efficiency [2], which is very much in the same ballpark. There is also some heat absorbed by the engine block, which is the other part of the spacecraft to be in direct sunlight. If you assume little reflection (ie. most of the light becomes either heat directly, or electricity, which will become heat after it is used by the spacecraft), you get about 915 kW of heat continually absorbed by the spacecraft while still close to Earth.

There’s one other potential source of heat, which is crew. They convert energy stored in their food to heat, so they represent an additional source that the previous calculations don’t take into account. A normal human on a 2000 calorie diet gives off 100W [4], so a crew of 100 people would give off an additional 10 kW. This is small compared to the 915kW of solar radiation the spacecraft must lose, so we don’t need to consider it further.

Where will this heat ultimately end up? In the steady state, with the spacecraft maintaining constant temperature, there are only two places for it to go. One is out into space as radiation (good!), and the other is into the propellant tanks, boiling off the liquid methane and liquid oxygen (bad!).

The ITS has two smaller tanks (called header tanks) inside the main one which store propellant for the long haul to Mars [5]. Thanks to our knowledge of the tank diameter [6] and this shot of the inside of the spacecraft [7], we can find the volume of the spherical liquid oxygen header tank to be about 100 cubic meters [2]. If you put all 915kW the spacecraft was absorbing into the liquid oxygen tank, you would lose all the propellant in about 7 hours [2]. Obviously this would be unworkable for a ~100 day transit time [8] that needs to use the propellant at the end of the journey to land on Mars, so to avoid this, the vast majority of the heat must be radiated into space.

Two surfaces will do most of this task: the solar panels and the hull. How much heat is radiated is a strong function of temperature (~T4), such that 10°C (18°F) warmer is about a 12% increase in heat radiated.

The temperature of the hull is constrained, though, because the same process that radiates heat into space also radiates it from the hull into the header tank. If you assume a tank that reflects 90% of the light that hits it [9], and that you only want to lose 10% of your fuel over 100 days, this means the hull must be kept at 127 Kelvin (-126°C, -195°F)[2], barely warmer than the propellant in the header tank.

This would represent very little radiation into space. If all the heat must be radiated by the panels, this puts them at a temperature of 346 Kelvin (73°C, 163°F)[2]. Although this is higher than a normal panel on Earth, it’s about the temperature that ISS solar panels operate at [9] when they’re at their hottest.

So this all appears consistent. The vast majority of the heat will be absorbed and radiated by the solar panels – the spacecraft may need heat pumps to ensure this takes place, but doing so involves no unreasonable extremes of temperature in the panels. The tank section will have to be kept much colder (blackbody radiation hitting the header tanks is only one part of it – conduction through the structural sections will also heat the tank to some extent), though the temperatures required for passive cooling suggests that some element of active refrigeration may also be needed. All in all, from a thermal management perspective at least, Musk’s plans to explore the Red Planet seem eminently realistic and feasible.

[1] From the IAC presentation, at 19:51.

[2] A notebook containing all of the calculations for this post.

[3] Based on the linked press release from SolarCity.

[4] This is simply a units conversion.

[5] From Musk’s r/SpaceX AMA (thanks to  /u/__Rocket__ for the question).

[6] Slide 29

[7] IAC presentation, 24:43

[8] Slide 37

[9] Page 13 – peak temperature is just under 200°F (93°C, 366 K)

6 thoughts on “Thermal Management Aboard the ITS

  1. Let me add an issue. They want to produce the propelant for the return trip on the Martian surface. An industry will exist for this purpose in the Martian city. For a early trips, however, the propellant must be made with minimal equipments. Probably, they want to store the return propellant in the tanks of the spacecraft during the process. That is, they have to store hundreds of tons of chilled liquid oxigen and methane and manage it thermally. Is it manageable?

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  2. A topic I have been looking into … per person you can plan on 300 btu http://www.tombling.com/cooling/heat-load-calculations.htm … I think you are seriously underestimating the heat load. The ISS has seven 2,470-pound HRS radiator assemblies and four 1650-pound PVR assemblies to NASA. The HRS Radiators comprise two wings of three assemblies each, one on either side of the ISS main truss. Each HRS assembly consists of eight panels measuring 9 ft. x 11 ft. When retracted in the launch configuration — folded accordion fashion — the radiator assemblies will fit easily into the payload bay of the Space Shuttle Orbiter. When attached to the ISS in orbit, each HRS assembly will extend to 11 ft. x 75 ft. via an electric motor driven “scissor” mechanism.Each HRS assembly is capable of rejecting at least 11.8 kilowatts of excess ISS heat, thereby providing cooling to the crew compartment, spacecraft subsystems and experiments. The Lockheed Martin Missiles and Fire Control – Dallas-produced radiator assemblies will mate with a pumped liquid ammonia heat transfer system to cool the ISS crew and equipment.

    The EATCS consists of two independent Loops (Loop A & Loop B), they both use mechanically pumped Ammonia in fluid state, in closed-loop circuits. The EATCS is capable of rejecting up to 70 kW, The PVTCS for the solar arrays adds another 56 kw of heat rejection so 126 kw in total. While the total solar arrays are capable of 120 kw (which by the way are not off the shelf .. you cannot make a useful comparison between commercial PV and designed for space… radically different)

    100 people on musks ship with support equipment is likely going to need 200-400 kw. For an analysis I am working on I settled on 350kw. Thermal management needs to be a redundant system, you cannot let it fail or everyone dies… from overheating not the cold. so spacex will need to plan on 600-700 kw of radiators or 11 ft x 4700 ft of radiator based upon the ISS design

    feel free to throw rocks at this … I am just trying to ferret out reality

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    1. Interesting. So my analysis is based on the solar power capacity stated by Musk in the ITS talk. Your estimate for 100 people’s power usage of 350W may be realistic (implying that the spacecraft will need some additional power source), but Musk has stated that early flights will have a reduced crew (~12): https://www.reddit.com/r/spacex/comments/590wi9/i_am_elon_musk_ask_me_anything_about_becoming_a/d94txm0/
      In the post I showed that the heat given off even by 100 humans is only 10kW, so it was too small to worry about compared to the other sources of heat – of course, it becomes less significant still with the smaller crew of the early flights.

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      1. It is the heat load of the equipment that will be the issue and you need to account for Sensible heat and Latent heat for air conditioning requirement which will turn the 10kw load for 100 people to 30kw of energy to manage it … then add physical activity (working out 2-4 hours per day and your 10kw has a load at 2 to 3 times this (people exercising will generate 300 watts each easily and their metabolic rate will stay elevated for hours after their exercise. The Latent heat load and sensible heat load could be 60kw-90kw.

        if you have a 200kw power consumption … 75% of that will need to be rejected as heat so between human activity and power consumption you are pushing 250kw without planning for redundancy in a life limiting support system… you are going to want at least 400kw of heat rejection capability to be safe and that is 3x the surface area of the ISS’s massive radiators (possibly lose 20% due to less reflected heat from earth …i would have to do the calcs but it isn’t that hard … i will let you know

        useful links
        http://www.engineeringtoolbox.com/persons-heat-gain-d_242.html
        http://www.engineeringtoolbox.com/heat-gain-equipment-d_1668.html
        http://www.engineeringtoolbox.com/met-metabolic-rate-d_733.html

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  3. you wanna do a real interesting analysis … go through the power requirements on mars and what your options are…. The main power consumption will come from sustainable farming. I am not going to go into the cost of the structure, water, recycling etc. Just the power. On Earth you are said to need 1 acre per person to feed that person reliably. I am reluctantly going to adopt a plan that only calls for 111 square meters per person. This is 36 times the farm productivity on earth. It doesn’t matter how the farming is actually done for this exercise, it can be aeroponics, it can be conventional farming.

    What is constant is the power per square foot using LED light sources. Aeroponics and indoor farming articles all indicate 50 watts per square foot as a recommended minimum. We can save a little perhaps with transparent growing structures but radiation might be counter productive so let’s just plan on growing the food shielded from the radiation. This equals 599kwh per person per day

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  4. Farming won’t be such a big problem, if cosmic ray can be filtered and plants feeded with lovely sunlight.

    The thermal management problem can be solved by heat exchange with boil off of cynogas, before discharge them into space. Simply utilize radiation can only take off heat partly

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